We are interested here in a theoretical and practical approach for detecting atypical segments in a multi-state sequence. We prove in this article that the segmentation approach through an underlying constrained Hidden Markov Model (HMM) is equivalent to using the maximum scoring subsequence (also called local score), when the latter uses an appropriate rescaled scoring function. This equivalence allows

In this paper, we investigate the optimal dividend problem under Parisian ruin with affine penalty payments at Parisian ruin time. The underlying risk process is assumed to be a spectrally negative Lévy risk process. With the help of the dynamic programming principle, we prove that the value function associated to our optimal control problem is the smallest solution with certain characteristics to

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating

The article studies the running maxima \(Y_{m,j}=\max_{1 \le k \le m, 1 \le n \le j} X_{k,n} - a_{m,j}\) where {Xk,n,k ≥ 1,n ≥ 1} is a double array of φ-subgaussian random variables and {am,j,m ≥ 1,j ≥ 1} is a double array of constants. Asymptotics of the maxima of the double arrays of positive and negative parts of {Ym,j,m ≥ 1,j ≥ 1} are studied, when {Xk,n,k ≥ 1,n ≥ 1} have suitable “exponential-type”

A hybrid preventive maintenance policy for heterogeneous degrading items is discussed. It combines the classical age-replacement strategy, when a system is replaced either on failure or at the predetermined age, with replacement of the system when degradation reaches the predetermined level at some intermediate time. Items come from two subpopulations with different reliability characteristics. Non-homogeneous

We consider an extended form of the MX/M/c queue with two types of server groups: Static as well as dynamic (which turn on/off in a state-dependent manner) servers. The two server groups may have homogenous or non-homogenous service rates. The model is further extended to feature setup and delayed-off times, finite capacity, and k staffing levels. This class of queues is solved via the difference equations

Consider a compound renewal risk model, in which a single accident may cause more than one claim. Under the condition that the common distribution of the individual claims is second order subexponential, we establish a second order asymptotic formula for the infinite-time ruin probability. Compared with the traditional ones, our second order asymptotic result is more precise and effective, which can

It has been observed in real networks that the fraction of nodes P(k) with degree k satisfies the power-law P(k) ∝ k−γ for k > kmin > 0. However, the degree distribution of nodes in these networks before kmin varies slowly to the extent of being uniform as compared to the degree distribution after kmin. Most of the previous studies focus on the degree distribution after kmin and ignore the initial

In this paper, we investigate several random structures, namely two classes of random lobster trees (RLTs) and a class of random spider trees (RSTs). The first class of RLTs grow with a fixed probability, whereas those from the second class evolve in a dynamic manner underlying a flavor of semi-opposite reinforcement. For these two classes, we characterize the structure of the random graphs therein

This paper presents a link between unbalanced non-linear urn model (a two-colored urn model) and stochastic approximation theory. Findings of our study reveal a successful establishment of limit laws for the urn composition, obtained under a drawing rule reinforced by an \(\mathbb {R}_{+}\)-valued concave function and a non-balanced replacement matrix.

We propose a method based on the Fourier transform for numerically solving backward stochastic differential equations. Time discretization is applied to the forward equation of the state variable as well as the backward equation to yield a recursive system with terminal conditions. By assuming the integrability of the functions in the terminal conditions and applying truncation, the solutions of the

This paper investigates the asset-liability management problem for an ordinary robust insurance system between a reinsurer and an insurer under the Heston model with delay. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium and invest its wealth in a financial market that contains a risk-free asset and a risky asset whose price process is described by the Heston model

In this paper, relations between some kinds of cumulative entropies and moments of order statistics are established. By using some characterizations and the symmetry of a non-negative and absolutely continuous random variable X, lower and upper bounds for entropies are obtained and illustrative examples are given. By the relations with the moments of order statistics, a method is shown to compute an

A periodic-review insurance model is studied under the following assumptions. One-period insurance claims form a sequence of independent identically distributed nonnegative random variables with a finite mean. At the beginning of each period a quota δ of the company surplus is invested in a non-risky asset for m periods. Theoretical expressions for finite-time and ultimate ruin probabilities, in terms

The present work proposes a new stationary integer-valued bilinear time series model with dependent counting series. The model will enable one to tackle the presence of some correlation between underlying events. The various probabilistic and statistical properties of the model are discussed, unknown parameters are estimated by several methods. Moreover, the performance of the estimation methods is

We present competing risks models within a semi-Markov process framework via the semi-Markov phase-type distribution. We consider semi-Markov processes in continuous and discrete time with a finite number of transient states and a finite number of absorbing states. Each absorbing state represents a failure mode (in system reliability) or a cause of death of an individual (in survival analysis). This

This paper is interested in studying a type of production models-stocks that can be seen as a stochastic fluid flow system with upward jumps at level zero. The joint distribution of the stocks level and the controlling Markov process is governed by two differential systems with specific boundary conditions. The uniqueness of the solution of this problem has been proved. Also, a unified solution with

Okisaka et al. (2017) investigated the eigen-distribution for multi-branching trees weighted with (a,b) on correlated distributions, which is a weak version of Saks and Wigderson’s (1986) weighted trees. In the present work, we concentrate on the studies of eigen-distribution for multi-branching weighted trees on independent distributions. In particular, we generalize our previous results in Peng et

We introduce the random exponential recursive tree in which at each point of discrete time every node recruits a child (new leaf) with probability p, or fails to do so with probability 1 − p. We study the distribution of the size of these trees and the average level composition, often called the profile. We also study the size and profile of an exponential version of the plane-oriented recursive tree

In this paper, a jump-diffusion Omega model with a two-step premium rate and a threshold dividend strategy is studied. For this model, the surplus process is a perturbation of a compound Poisson process by a Brownian motion. Firstly, using the strong Markov property, the integro-differential equations for the expected discounted dividend payments function, the Gerber-Shiu expected discounted penalty

In this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems’ lifetimes are obtained

The Markov renewal process (MRP) of M/G/1 type has been used for modeling many complex queueing systems with correlated arrivals and the special types of transitions of the MRP process corresponds to the departures from the queueing system. It can be seen from the central limit theorem for regenerative process that the distribution of the number of transitions of MRP is asymptotically normal. Thus

A matrix variate generalization of the two-sided power distribution is proposed. Several properties of this distribution including probability density function, cumulative distribution function and characteristic function are derived.

This paper presents several numerical applications of deep learning-based algorithms for discrete-time stochastic control problems in finite time horizon that have been introduced in Huré et al. (2018). Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control

We analyze a multi-processor two-stage tandem call center retrial queueing network in which the processors are subject to active breakdowns and repairs at stage-I. A level-dependent quasi-birth-and-death (LDQBD) process is formulated and a sufficient condition for ergodicity of the system is discussed. Under the stability condition, the stationary distribution of the number of calls in the system,

We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error for this class of estimators. Further, we propose a parametric technique for estimating optimal batch sizes and discuss practical issues regarding the estimating process

A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GIX/Geo/c/N is presented. In the past, various discrete-time queueing models, particularly the multi-server bulk-arrival queues with finite-buffer have been solved using complicated methods that lead to results in a non-explicit form. The purpose of this paper is to present a

Many hedge funds and retail investors demand volatility and variance derivatives in order to manage their exposure to volatility and volatility-of-volatility risk associated with their trading positions. The Heston model is a standard popular stochastic volatility model for pricing volatility and variance derivatives. However, it may fail to capture some important empirical features of the relevant

Poisson processes are widely used to model the occurrence of similar and independent events. However they turn out to be an inadequate tool to describe a sequence of (possibly differently) interacting events. Many phenomena can be modelled instead by Hawkes processes. In this paper we aim at quantifying how much a Hawkes process departs from a Poisson one with respect to different aspects, namely,

Association or interdependence of two stock prices is analyzed, and selection criteria for a suitable model developed in the present paper. The association is generated by stochastic correlation, given by a stochastic differential equation (SDE), creating interdependent Wiener processes. These, in turn, drive the SDEs in the Heston model for stock prices. To choose from possible stochastic correlation

In this article we investigate the performance of scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional normal data, in presence of outliers, when the population variance is unknown. For fixed window scan statistics, both the training sample and parametric bootstrap methods are employed for one and two dimensional normal

We propose a class of evolution models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and after that a genome is removed according to the selection scheme that involves fitness. Thus, the population size remains constant. The process evolves according to a Markov chain

The original version of this article contained mistakes, and the author would like to correct them.

Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its

We present a new approach to study big data in finance (specifically, in limit order books), based on stochastic modelling of price changes associated with high-frequency and algorithmic trading. We introduce a big data in finance, namely, limit order books (LOB), and describes them by Lobster data-academic data for studying LOB. Numerical results, associated with Lobster and other data, are presented

In this paper we consider a single server queueing model with under general bulk service rule with infinite upper bound on the batch size which we call group clearance. The arrivals occur according to a batch Markovian point process and the services are generally distributed. The customers arriving after the service initiation cannot enter the ongoing service. The service time is independent on the

The Hartman-Watson distribution with density \(f_{r}(t)=\frac {1}{I_{0}(r)} \theta (r,t)\) with r > 0 is a probability distribution defined on \(t \in \mathbb {R}_{+}\), which appears in several problems of applied probability. The density of this distribution is given by an integral θ(r, t) which is difficult to evaluate numerically for small t → 0. Using saddle point methods, we obtain the first

It is well known that the empirical distribution function has superior properties as an estimator of the underlying distribution function F. However, considering its jump discontinuities, the estimator is limited when F is continuous. Mixtures of the binomial probabilities relying on Bernstein polynomials lead to good approximation properties for the resulting estimator of F. In this paper, we establish

A specific function f(r) involving a ratio of complicated gamma functions depending upon a real variable r(> 0) is handled. Details are explained regarding how this function f(r) appeared naturally for our investigation with regard to its behavior when r belongs to R+. We determine explicitly where this function attains its unique minimum. In doing so, quite unexpectedly the customary Cramér-Rao inequality

This paper analyzes an infinite-buffer single-server bulk-service queueing system in which customers arrive according to a discrete-time renewal process. The customers are served under the discrete-time Markovian service process according to the general bulk-service rule. The matrix-geometric method is used to obtain the queue-length distribution at prearrival epoch. The queue-length distributions

The best known result about the joint distribution of the backward and forward recurrence times in a renewal process concerns the asymptotic behavior for the tail of that bivariate distribution. In the present paper we study the joint behavior of the recurrence times at a fixed time point t, and we obtain both exact results and bounds for their joint tail behavior. We also obtain results about the

This work is concerned with a novel stochastic competitive model with saturation effect and distributed delay, in which two coupling noise sources are incorporated and the interspecific competition delayed terms show saturation effect. A good understanding of exponential extinction, extinction, persistence in the mean and permanence in time average of two species are gained. Also, with the help of

This article provides a novel method to solve continuous-time semi-Markov processes by algorithms from discrete-time case, based on the fact that the Markov renewal function in discrete-time case is a finite series. Bounds of approximate errors due to discretization for the transition function matrix of the continuous-time semi-Markov process are investigated. This method is applied to a reliability

In this paper, we study the properties of a sequential maximum likelihood estimator of the unknown parameter for the squared radial Ornstein-Uhlenbeck process. The estimator is proved to be closed, unbiased, normally distributed and strongly consistent. Lastly a simulation study is presented to illustrate the efficiency of the estimators.

We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal distributions, conditional distributions, linear transformations, characteristic functions and dependence measure in the perspective of the inconsistency property. In

We consider continuous-time Markov branching processes in semi-Markov random environment and obtain diffusion approximation results for the near critical case. The problem of semi-Markov environment, presented here, is new and more interesting than the Markov case, since it includes many particular interesting cases: Markov, renewal, etc. The particular case of the Markov random environment of continuous-time

The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation

In this paper we show how to extend a simple common shock model with Archimedean dependence of the hidden variables to the non-exchangeable case. The assumption is that the hidden risk factors are linked by a hierarchical Archimedean dependence structure, possibly fully nested. We give directions about how to implement the model and to address the issue that the hidden variables must be put in descending

We consider the classical Cramér-Lundberg risk model with claim sizes that are mixtures of phase-type and subexponential variables. Exploiting a specific geometric compound representation, we propose control variate techniques to efficiently simulate the ruin probability in this situation. The resulting estimators perform well for both small and large initial capital. We quantify the variance reduction

This paper studies the coupon subset collection problem with quotas, which is a variant of the classical coupon-collection problem. Specifically, the set of coupons is divided into distinct subsets, each of which is referred to as a class and each element of a class is referred to as a type. Coupons can be collected one by one by purchasing a coupon package. A coupon class is said to be acquired if

In the present paper we study the distributions of families of patterns which generalize runs and patterns distributions extensively examined in the literature during the last decades. In our analysis we assume that the sequence of outcomes under investigation includes independent, but not necessarily identically distributed trials. An illustration is also provided how our new results could be exploited

In this paper, we propose proximal splitting-type algorithms for sampling from distributions whose densities are not necessarily smooth nor log-concave. Our approach brings together tools from, on the one hand, variational analysis and non-smooth optimization, and on the other hand, stochastic diffusion equations, and in particular the Langevin diffusion. We establish in particular consistency guarantees

The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov regime switching. The optimal control problem is presented by making use of dynamic programming. In the case where the Markov chain has two states, the optimal homotopy analysis method (OHAM) is used to obtain an analytical approximation of the value function

The paper focuses on a new method for the inference of a parametric random spheroid from the observations of its 2D orthogonal projections. Such a stereological problem is well-known from the literature when the projections come from only one deterministic spheroid. Nevertheless, when the spheroid is random itself, the estimation of its distribution is not straightforward. From a theoretical viewpoint

In this article, we consider random occupancy models and the related problems based on the methods of generating functions. The waiting time distributions associated with sequential random occupancy models are investigated through the probability generating functions. We provide the effective computational tools for the evaluation of the probability functions by making use of the Bell polynomials.

Mobile crowd sensing is a widely used sensing paradigm allowing applications on mobile smart devices to routinely obtain spatially distributed data on a range of user attributes: location, temperature, video and audio. Such data then typically forms the input to application specific machine learning tasks to achieve objectives such as improving user experience, targeting geo-localised query based searches

The time and cost to start a business are highly related to the degree of transparency of business information, which strongly impacts the loss due to illicit financial flows. In order to study the distributional characteristics of time and cost to start a business, we introduce right-truncated and left-truncated T-X families of distributions. These families are used to construct new generalized families

Asymptotic unbiasedness and L2-consistency are established for various statistical estimates of mutual information in the mixed models framework. Such models are important, e.g., for analysis of medical and biological data. The study of the conditional Shannon entropy as well as new results devoted to statistical estimation of the differential Shannon entropy are employed essentially. Theoretical results

We consider a telegraph process with elastic boundary at the origin studied recently in the literature (see e.g. Di Crescenzo et al. (Methodol Comput Appl Probab 20:333–352 2018)). It is a particular random motion with finite velocity which starts at x ≥ 0, and its dynamics is determined by upward and downward switching rates λ and μ, with λ > μ, and an absorption probability (at the origin) α ∈ (0

In this paper we propose a generalisation to the Markov Arrival Process (MAP) risk model, by allowing for a delayed receipt of required capital injections whenever the surplus of an insurance firm is negative. Delayed capital injections often appear in practice due to the time taken for administrative and processing purposes of the funds from a third party or the shareholders of a firm. We introduce